The probability that the number of heads obtained from flipping the two fair coins is the same is 35/128.
Probability:
Probability means the fraction of favorable outcome and the total number of outcomes.
So it can be written as,
Probability = Favorable outcomes / Total outcomes
Given,
The coin a is flipped three times and coin b is flipped four times.
Here we need to find the probability that the number of heads obtained from flipping the two fair coins is the same.
We know that,
There are 4 ways that the same number of heads will be obtained;
0, 1, 2, or 3 heads.
The probability of both getting 0 heads is
[tex]$\left(\frac12\right)^3{3\choose0}\left(\frac12\right)^4{4\choose0}=\frac1{128}$[/tex]
Probability of getting 1 head,
[tex]$\left(\frac12\right)^3{3\choose1}\left(\frac12\right)^4{4\choose1}=\frac{12}{128}$[/tex]
Probability of getting 2 heads is,
[tex]$\left(\frac12\right)^3{3\choose2}\left(\frac12\right)^4{4\choose2}=\frac{18}{128}$[/tex]
And the probability of getting 3 heads is,
[tex]$\left(\frac12\right)^3{3\choose3}\left(\frac12\right)^4{4\choose3}=\frac{4}{128}$[/tex]
Therefore, the probability that the number of heads obtained from flipping the two fair coins is the same is,
=> (1/128) + (12/128) + (18/128) + (4/128)
=> 35/128.
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The inventor of a new game believes that the variable cost for producing the game is $0.50 per unit and the fixed costs are $4,300. the inventor sells each game for $1.89. let x be the number of games produced. (a) the total cost for a business is the sum of the variable cost and the fixed costs. write the total cost c (in dollars) as a function of the number of games produced. c = (b) write the average cost (in dollars) per unit c = c x as a function of x. c =
The total cost is represented as C = $0.50x + $4300 and the average cost as avgC = $0.50 + $4300/x
We have been given that,
The variable cost for producing the game = $0.50 per unit
The fixed cost for producing the game = $4300
Let the total cost be denoted by C.
And let x be the number of games produced.
a) Total cost = variable cost + fixed cost
C = $0.50x + $4300
b) Average cost = total cost/number of games produced
= C/x
= ($0.50x + $4300)/x
= $0.50 + $4300/x
Hence the total cost is C = $0.50x + $4300 and the average cost is $0.50 + $4300/x
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PLEASE HELPPPPPPPPPP
Answer:
20 1/16
Step-by-step explanation:
please give brilliantest pls
Answer:
You have the correct answer [tex]20 \frac{1}{16}[/tex]
Step-by-step explanation:
Rhiannon and Sophie both started saving for a new piano this month. Rhiannon will deposit $35.80 per week, but her bank account is currently overdrawn with a -$253.50 balance. Sophie also has a negative bank account balance of -$78.25 and will deposit $23.30 each week. How many weeks (w) will it take for the two bank accounts to have the same balance?
It will take 14.02 weeks for both the accounts to have the same balance
Bank account balance of Rhiannon = -$253.50
Money deposited by Rhiannon in the bank account each week = $35.80
Bank account balance of Sophie = -$78.25
Money deposited by Sophie in the bank account each week = $23.30
Let the number of weeks it takes to have the same account balance be x, therefore formulating the algebric equation we get:
Bank balance of Rhiannon + Money deposited by her each week*No of weeks it will take for the balance to be equal = Bank balance of Sophie + Money deposited by her each week*No of weeks it will take for the balance to be equal
= -253.5 + 35.8(x) = -78.25 + 23.3(x)
= -175.25 = -12.5(x)
x = 14.02 weeks
Therefore, it will take 14.02 weeks for both the accounts to have the same balance
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Find FH
FH = {Blank}
Answer:
22
Step-by-step explanation:
By the segment addition postulate, FH=8+14=22.
The equation will be,
→ FH = FG + GH
Then the value of FH will be,
→ FH = 8 + 14
→ [ FH = 22 ]
Hence, the value of FH is 22.
GUYS HELP 4-10! ASAP IF YOU CAN EXPLAIN STEP MY STEP SO I CAN UNDERSTAND NEED MY GRADES UP! PLEASE HELP Please help. I need to get my grades up so the help would really mean a lot!
Step-by-step explanation:
so, the best way to help you is to help you understand how to solve such problems yourself.
let me know if you still don't understand something :
4.
this you can solve just by common sense.
let's see if you understand it with smaller numbers :
1 ball costs $3. how much will 2 balls cost ? well, twice as much : 2×3 = $6.
how much will 3 balls cost ? hmmm ? three times as much : 3×3 = $9.
and so on.
so, how much will 10 balls cost ? right, ten times a much : 10×3 = $30.
now,
8 eggs for 3 cups of flour.
how many eggs for 30 cups of flour ? you notice that 30 is 10 times 3, right ?
yes, ten times a many eggs : 10×8 = 80 eggs.
5.
3 quarters simply means 3/4.
if we want to know how much 3/4 of something is, we have to multiply that something by 3/4.
so, for 60 students :
60 × 3/4 = 180/4 = 45 students bring a lunch from home.
6.
similar to 4.
5 books in 2 days.
how many books in 8 days ?
you notice that 8 is 4 times 2 ?
so, yes, 4 times as many books : 4×5 = 20 books.
7.
now we are getting into areas, where we need more thinking and apply formal mathematics.
10 pounds jam requires 5 pounds apples.
8 pounds jam require x pounds apples.
the easiest way is to use ratios :
jam to apples = 10/5 = 2/1 = 2
8 pounds jam to x pounds apples must follow the same ratio, as we are using the same recipe.
8/x = 2
8 = 2x
x = 4
so, to get 8 pounds of jam we need 4 pounds of apples.
8.
it seems they were very, very hungry ...
Jenny ate 6 1/4 pizzas.
Dolly ate 5 1/4 pizzas.
6 1/4 = (6×4 + 1)/4 = 25/4
5 1/4 = (5×4 + 1)/4 = 21/4
so, Jenny ate 25/4 / 21/4 = 25/21 = 1.19047619... times more pizza.
or in other words she ate
25/4 - 21/4 = 4/4 = 1 more pizza.
9.
so, he wins 5 of every 15, that is a ratio of 5/15 = 1/3.
he had 75 matches. 1/3 of 75 matches (see also 5.) means
75 × 1/3 = 75/3 = 25.
he won 25 matches.
10.
Mrs. Paul is 145 cm tall.
the daughter is 1/5 of that. see 5. and 9. :
1/5 of 145 means
145 × 1/5 = 145/5 = 29 cm
her daughter is 29 cm tall (a baby).
What is the difference between -21 and -8?
Answer:
-13
Step-by-step explanation:
(-21) - (-8) = -13
-21 - -8 = -13
Because of the two subtract signs next to each other before the number 8, they change to an addition sign.
From -21, move right 8 places along the number line because it is add 8.
-21 -20 -19 -18 -17 -16 -15 -14 -13
And you get to -13
Therefore, -21 + 8 = -13
HELPP DUE TODAY
Geometry bisectors
Answer:
Step-by-step explanation:
Bisects means that ∠RED will be divided in two parts by segment EB. This means that ∠REB = ∠BED. So,
5x-3 + 5x-3 = 8x+16
10x-6 = 8x+16
2x = 22
x = 11
Keep in mind that 11 is NOT the angle of ∠BED. You will plug it back into ∠REB to get
5(11)-3 = 52
Therefore, ∠BED = 52°
44 < 5x6 and 5x - 6 ≤ 54
Answer:
5x - 6 ≤ 54
5x-6+6 ≤ 54+6
5x ≤ 60
divide by 5
x ≤ 12
Step-by-step explanation:
Alyse bought 1/3lb of orange pekoe tea and 1/2lb of
English cinnamon tea. How many pounds of tea did
she buy?
According to the solving Alyse buy 5/6lb pounds fraction of tea.
What in math is a fraction?A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator as well as denominator of a complex fraction is a fraction.
How come a fraction is a number?A numerator, which is located above the line, and a denominator make up fractions (which is below the line). You may find out how many equally sized pieces are divided into something by looking at the denominator. How many of these equal components are taken into account is indicated by the numerator.
According to the given fraction:1/3lb of orange pekoe tea.
1/2lb of English cinnamon tea.
find the total pound of tea she buy:
So,
Adding these two fraction we get the total pounds:
= [tex]\frac{1}{3} + \frac{1}{2}[/tex]
= [tex]\frac{2 + 3}{6}[/tex]
= 5/6 lb
According to the solving Alyse buy 5/6lb pounds of tea.
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I am willing to give a brainliest to anybody, just please help !!!
During which game is she more effective serving?
How did you find this answer and please show your work?
Answer: The First game with 16/19 serves
Step-by-step explanation: Fraction also means division. So once you divide both fractions, you'll see that 16/19 > 13/16. That shows that she was more effective in the first game.
i need help please thanks
Answer:
the answer is the answer of the answer okay answer
Step-by-step explanation:
the answer is the answer of the answer okay aanswer
Puzzle #4
1: Find the slope:
3: Find the slope:
(2,-6), (-4, -3)
2: Find the slope:
X
Y
-1
-12
1
-8
-4
0
35
5
4: Find the slope:
answer choices
B:
A:
C:
m=-2 m=0 m = 2
D:
m = -4
G:
m=
undefined
E: IF:
m =-
2
m = 4
I
H: -I:
m =
2
m =
Type the 4-
letter code into
the answer
box. All CAPS,
no spaces.
Does anyone know the code to puzzle 4???? Please
Answer:
1/-2
Step-by-step explanation:
Slope(m) = y2- y1/x2-x1
= -3-(-6)/-4-2
=+3/-6
=1/-2
how many 20mm long wire pieces could be cut from a 1 meter long wire piece
Multiply. 6/7 ⋅ 4/15
A. 8/35
B. 14/45
C. 5/11
D. I don't know
Answer:
A
Step-by-step explanation:
Multply = 24/105
Divide by 3
8/35
Systems by elimination
2x - y = 2
-8x + 4y = −8
Answer:
Infinitely many solutions.
Step-by-step explanation:
Let's solve your system by elimination.
2x−y=2;−8x+4y=−8
Multiply the first equation by 4,and multiply the second equation by 1.
4(2x−y=2)
1(−8x+4y=−8)
Becomes:
8x−4y=8
−8x+4y=−8
Add these equations to eliminate x:
0=0
Given that
3x8 7:2
Calculate the value of x.
Give your answer in its simplest form.
X =
The value of x in the equation is x = -8/30
What are linear equations?Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the value of x?The equation is given as
3x + 8 = 7.2
Subtract 8 from both sides of the equation
3x = -0.8
Divide both sides by 3
x = -0.8/3
Rewrite as
x = -8/30
Hence, the value of x in the equation is x = -8/30
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how many different letter arrangements can be obtained from the letters of the word statistically, using all the letters?
Different letter arrangements that can be obtained from the letters of the word statistically, using all the letters= 6,48,64,800
Given,
Total number of arrangements obtained = 6,48,64,800
Given words = STATISTICALLY
Total word count = 13
Here we have repeated alphabets as -
"S"s = 2
"T"s = 3
"A"s = 2
"I"s = 2
"L" = 2
Total permutations we have here = 13! / 2!2!2!2!3!
= 6,22,70,20,800 / 96
= 6,48,64,800
What is Permutation?A permutation of a set in mathematics is, broadly speaking, the rearranging of its components if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."
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Pleasee help I need the answer rn
I'll give you the answer if you cas ap $2
Write the fraction 12/28 in simplest form.
Answer:
3/7
Step-by-step explanation:
12/28=3*4/4*7=3/7
It took Jane 3.5 hours to write 1 paper. At this rate, how long would it take Jane to write all 8 of her papers due this semester?
Find the least common denominator (LCD) of 5/6 and
8/9
please im begging you help me
Answer: Translation means you move a shape without rotating or flipping it and reflection is a mirror image of the shape. In the current example, the shape is translated right and down a noncalculable amount.
CRAFT FAIR Kylie is going to try to sell two of her oil paintings at the local craft fair. She is hoping to earn at least $400.
a. Write the inequality that represents the constraint of the situation, where x is the price of the first oil painting, and y is the price of the second.
b. Graph the inequality that represents the constraint on the sale.
The inequality that represents the constraint of the situation is x+y ≥ 400.
Inequality is defined as the mathematical expression in which both sides are not equal .
In inequalities the two vales are compared by "≤" , "≥" , "≠" .
For Example : 2x+3y≥4 is an example of inequality .
In the given question
Part (a)
Given Kylie sell first oil painting in $x
and second oil painting in $y.
Kylie is trying to earn at least $400.
the term at least means she can earn $400 or greater than $400, so ≥ sign will be used,
According to the question
we get , x+y ≥ 400
So , x+y ≥ 400, is the inequality that represents the constraint of the situation.
Part (b)
The Graph of the inequality x+y ≥ 400 that represents the constraint on the sale is shown below .
Therefore , the inequality that represents the constraint of the situation is x+y ≥ 400.
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Help?? The answer isn't -1026 btw i already guessed :(
Answer:
153
Step-by-step explanation:
12² - 3 [ 4([tex]\frac{1}{4}[/tex] - [tex]1^{8}[/tex] ) ] ← evaluate the inside part of the bracket
= 144 - 3 [ 4([tex]\frac{1}{4}[/tex] - 1) ]
= 144 - 3 [ 1 - 4 ]
= 144 - 3(- 3)
= 144 + 9
= 153
Rewrite the Expressions using Distributive Property
(2+3)6
Answer:
Step-by-step explanation:
If you distribute 6 to the numbers inside the parenthesis, it means that you multiply both number by 6
2 x 6 = 12
3 x 6 = 18
the expression can be rewritten like the following:
12 + 18 = 30
Given [tex]f(x)=\frac{1}{x+5}[/tex], find the average rate of change of f(x) on the interval
[1,1+h]. Your answer will be an expression involving h.
Pls halp
The average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
How to find the average rate of change of f(x) on the interval [1,1+h]?The function is given as
f(x) = 1/(x + 5)
The interval is given as
[1, 1 + h]
Calculate f(1) as follows
So, we have
f(1) = 1/(1 + 5)
f(1) = 1/6
Calculate f(1 + h) as follows
So, we have
f(1 + h) = 1/(1 + h + 5)
f(1 + h) = 1/(h + 6)
The average rate of change of f(x) on the interval [1,1+h] is then calculated as
Rate = [f(1 + h) - f(1)]/[1 + h - 1]
This gives
Rate = [1/(h + 6) - 1/6]/h
Hence, the average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
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helpppp plssssssssss
Answer:
x=2
Step-by-step explanation:
11-2x=5x-3
the first step, move the 3 over
14-2x=5x
In the second step moves 2x over
14=7x
finally, we just isolate the x from 7 by dividing 7
14/7=7x/7
simplify
2=x or x=2
Answer:
x=2
Step-by-step explanation:
*Shown two ways to solve.
11-2x=5x-3
+2x +2x
11=7x-3
+3 +3
14=7x
Divide by 7.
2=x
11-2x=5x-3
-11 -11
-2x=5x-14
-5x -5x
-7x=-14
Divide by -7.
x=2
Check to see if you're right.
11-2(2)=5(2)-3
11-4=10-3
7=7
Yep, it's correct.
Hope this helps.
What’s the next number in the pattern, and what is the formula to find the next 2 numbers in the pattern?
7, 28, 63, 112.. 175..
Answer: 7, 28, 63, 112, 175, 252, 343, ...
Step-by-step explanation:
7, 28, 63, 112, 175
7*1, 7*4, 7*9, 7*16, 7*25, ...
7*1², 7*2², 7*3^2, 7*4², 7*5²
Hence, 7n², n=1, 2, 3, 4, ...
7*6²=
7*6*6=
252
7*7²=
7*7*7=
343
Thus,
7, 28, 63, 112, 175, 252, 343, ...
Answer:
good luck brooooooooooo
what is 5,435,778 expressed in scientific notation? a.5.435778 x 10 b.5.435778 x 10 c.5.435778 x 10 d.5.435778 x 10
5,435,778 in scientific notation will be 5.435778×10⁶.
Scientific notation is the way to represents huge numbers in simple form. This ease understanding and calculation of the numbers. When written in a scientific notation, the number is called coefficient, the number to which power is raised is called base and raised power is called exponent. For instance, in the given answer, 5.435778 is coefficient, 10 is base and 6 is exponent.
While converting the numbers into scientific notation, we need to remember following points -
If the number is greater than 1 or is a multiple of 10, the decimal will be placed on the Left Hand Side. Like in the number in question, decimal moved to left and we got positive exponent. If the number is less than 1, then decimal will be placed at Right Hand Side. In this case, the exponent will be negative. For instance, we will represent 0.005 as 5*10-³.Learn more about scientific notation -
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The complete question is -
what is 5,435,778 expressed in scientific notation? a.5.435778 x 10⁷ b.5.435778 x 10³ c.5.435778 x 10⁶ d.5.435778 x 10⁵
s it true that for any integer n ≤ 2, φ(n) has a primitive root? if so, prove it. if not, give an explicit counterexample
No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root
What is primitive root?In modular arithmetic, a number g is called a primitive root modulo n if every number coprime to n is congruent to a power of modulo . Mathematically, g is a primitive root modulo n if and only if for any integer a such that gcd(a, n)=1 , there exists an integer k such that:
.[tex]g^{k}[/tex]≡ a (mod n)
Now,
Existence of Primitive root modulo n exists if and only if:
n is 1, 2, 4, orn is power of an odd prime number , orn is twice power of an odd prime number .So,
if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.
For example,
As ϕ(11)=10, the order of 2(mod11) must divide 10.
So we check 22≡4(mod11) and 25≡10(mod11).
Since neither of these are 1, and
we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,
ord112=ϕ(11), making 2 a primitive root modulo 11.
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